Emulation is the process of simulating the hardware of one computer (particularly the processor) via software on a different one. In other words, it allows you to use software meant for another system that you may not have access to by running a program on your system. For instance, an emulator will let you use an arcade machine that no longer exist or use a game console that can no longer be purchased.
Note that this category is different from Computers: Emulators because the focus here is on the emulation of general gaming purpose computers (also called consoles) and arcade machines.